ChinaGrid Supporting Platform (CGSP) is a core Grid middleware developed for the construction of ChinaGrid. CGSP provides the infrastructure services and the sets of tools to facilitate the seamless use and management of distributed, heterogeneous resources. Execution management, an important function module in CGSP, enables applications to have coordinated access to underlying resources, regardless of their physical location or access mechanism. Execution management is concerned with the problems of instantiating and managing, to completion, units of work (jobs). In CGSP, we provide the execution managements of two categories of atomic job (legacy program job and hyper-service job) and two categories of composite job (workflow job and GridPPI job). In this paper, we will in detail describe the design architecture and key aspects of implementation of execution management in CGSP.